Dissecting the question stem: we need info about x and y! When we're dealing with exponents, we always want to remind ourselves that positive fractions can cause wacky things to happen.beater wrote:If x and y are positive, is x^3 > y?
(1) sqrt x > y
(2) x > y
(1) sqrtx > y
We could choose x = 100 and y = 2, since 10 > 2.
Is 100^3 > 2? yes!
We could also choose x = 1/4 and y = 1/3, since 1/2 > 1/3.
Is (1/4)^3 > 1/3? no!
We can get a "yes" and a "no": insufficient.
(2) x > y
We could choose x = 100 and y = 2, since 100 > 2.
Is 100^3 > 2? yes!
We could choose x = 1/2 and y = 1/3, since 1/2 > 1/3.
Is (1/2)^3 > 1/3? no!
We can get a "yes" and a "no": insufficient.
Neither statement is sufficient alone, so we need to combine. Accordingly, we now know that:
sqrtx > y
and
x>y
We can still get a "yes" answer by choosing x = 100 and y = 2.
We're no longer allowed to pick x = 1/4 and y = 1/3, since those numbers violate statement (2).
However, we can still pick x = 1/2 and y = 1/3, since sqrt(1/2) > 1/3 and get our "no" answer.
Therefore, we can still get both a "yes" and a "no" answer: even together, not enough information, choose (e).
